Question

Gas turbine engines like those of jet aircraft operate on a
thermodynamic cycle known as the Brayton cycle. The basic Brayton
cycle, as shown in the figure, consists of two adiabatic
processes—the compression and the expansion of gas through the
turbine—and two isobaric processes. Heat is transferred to the gas
during combustion in a constant-pressure process (path from point 2
to point 3) and removed from the gas in a heat exchanger during a
constant-pressure process (path from point 4 to point 1). The key
parameter for this cycle is the pressure ratio, defined as
rp = pmax/pmin ≡ p2/p1,
and this is the only parameter needed to calculate the efficiency
of a Brayton engine.

(a) Determine an expression for the efficiency.
(Use the following as necessary: rp and
γ.)ε = ?

(b) Calculate the efficiency of a Brayton engine that uses a
diatomic gas and has a pressure ratio of 13. (Do not express your answer in
percent.)